TL;DR Exploring one of the most magical and versatile ingredients: Eggs.

Eggs as Eggs

Scrambled: Mixed eggs in a pan, sometime with cream or milk added, cooked either soft or hard

Fried/Sunny Side Up: A whole egg cracked into a pan and cooked to desired doneness

Hard-Boiled: A whole egg cooked in boiling water until the white and yolk are both fully cooked

Soft-Boiled: A whole egg cooked in boiling water until the white is cooked but the yolk is still runny

Omelettes: Mixed eggs in a pan, sometime with cream or milk added, cooked either soft (french style) or hard

Deviled: Eggs boiled, the the yolk separated and mixed with mayo, mustard, and other flavorings

Poached: eggs cracked into simmering water to cook with a set white and runny yolk

Egg Salad: boiled egg made into a salad mixed with mayo, mustard, and other flavorings

Frittata/Quiche: eggs baked with other ingredients

Pickled: Boiled egg preserved in salt, vinegar, and other flavorings

Salted: Boiled eggs preserved in a egg brine

Steamed (Chawanmushi): Egg steamed to a custard consistency with flavorings such as soy sauce

Eggs as Supplements

Batters – Eggs used to hold ingredients together (See: Fried Chicken)

Coatings – eggs (specifically whites) used to had a light coating to food (See: Chili Relleno)

Emulsions – egg yolks used to mix fat and other flavors together to get a creamy sauce (See: Hollandaise)

Stabilizers – egg whites used to hold ingredients together (See: Foams)

Thickeners – Eggs used to had viscosity to dishes  (See: Egg Nog)